In this paper a method is explained for finding a 14th independent point on E, which is defined over k(z), with [k:Q]=2. The method is applied to Nagao's curve. For this curve one has k=Q(sqrt{-3}).

The curves E and 13 of the 14 independent points are already defined over a smaller field k(t), with [k(z):k(t)]=2. Again for Nagao's curve it is proved that the rank of E(\bar Q(t)) is exactly 13, and that rank E(Q(t)) is exactly 12.

- rnk14.dvi (33104 bytes) [1997 Sep 16]
- rnk14.dvi.gz (14825 bytes)
- rnk14.ps.gz (62540 bytes)

Jasper Scholten <jasper@math.rug.nl>